JDK，Apache commons math里都没有发现组合函数，因而自己写了一个。

首先定义接口

package math.combination;

import java.util.Collection;
import java.util.List;

/**
 * the interface for combination
 * @author jhren
 *
 * @param <T>
 */
public interface Combinationable<T> {
	/**
	 * get combinations from start to end [start, end]
	 * it equals findCombiantions(start),findCombiantions(start+1), 
	 * ......
	 * findCombinations(end-1), findCombinations(end)
	 */
	public List<List<T>> findCombinations(int start, int end);
	/**
	 * get all combinations
	 * it equals findCombinations(0, size)
	 */
	public List<List<T>> findCombinations();
	
	/**
	 * find a combinations for size
	 * @param size
	 * @return
	 */
	public List<List<T>> findCombinations(int size);
	
	public Collection<T> getElements();
}

第一个个实现，输出的组合会按照类型T升序排列

例如输入为[3,2,1]的全组合为

[]
[3]
[2]
[1]
[2, 3]
[1, 3]
[1, 2]
[1, 2, 3]

package math.combination;

import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.List;

/**
 * the T should be Comparable the T in one combination list is sort by the
 * Comparable T
 * 
 * @author jhren
 * 
 * @param <T>
 */
public class ComparableCombination<T extends Comparable<? super T>> implements
		Combinationable<T> {

	private Collection<T> elements = new ArrayList<T>();

	public ComparableCombination(Collection<T> elements) {
		this.elements.addAll(elements);

	}

	@Override
	public List<List<T>> findCombinations(int start, int end) {
		if (start < 0) {
			throw new IllegalArgumentException("start can't be negative: "
					+ start);
		}
		if (end > elements.size()) {
			throw new IllegalArgumentException(
					"end can't be larger than elements size: " + end + ">"
							+ elements.size());
		}
		if(start > end) {
			throw new IllegalArgumentException(
					"start can't be larger than end: " + start + ">"
							+ end);
		}
		List<List<T>> result = new ArrayList<List<T>>();

		for (int i = start; i <= end; i++) {
			result.addAll(findCombinations(i));
		}

		return result;
	}

	@Override
	public List<List<T>> findCombinations() {
		return findCombinations(0, elements.size());
	}

	@Override
	public List<List<T>> findCombinations(int size) {
		if (size < 0) {
			throw new IllegalArgumentException("size can't be negative: "
					+ size);
		}
		if (size > elements.size()) {
			throw new IllegalArgumentException(
					"size can't be larger than elements size: " + size + ">"
							+ elements.size());
		}

		List<List<T>> result = new ArrayList<List<T>>();

		if (size == 0) {
			result.add(new ArrayList<T>());
			return result;
		}

		List<List<T>> combinations = findCombinations(size - 1);
		for (List<T> combination : combinations) {
			for (T element : elements) {
				if (combination.contains(element)) {
					continue;
				}

				List<T> list = new ArrayList<T>();

				list.addAll(combination);

				if (list.contains(element))
					continue;

				list.add(element);
				Collections.sort(list);

				if (result.contains(list))
					continue;

				result.add(list);
			}
		}

		return result;

	}

	@Override
	public Collection<T> getElements() {
		return elements;
	}

}

第二个实现，会保持元素的输入顺序

例如输入为[3,2,1]的全组合为

[]
[3]
[2]
[1]
[3, 2]
[3, 1]
[2, 1]
[3, 2, 1]

package math.combination;

import java.util.ArrayList;
import java.util.Collection;
import java.util.Iterator;
import java.util.List;




/**
 * the T in one combination list is sort by the input sequence
 * @author jhren
 *
 * @param <T>
 */
public class CombinationSortByInput<T> implements Combinationable<T> {
	static private class Element<E> implements Comparable<Element<E>> {
		private int rank;
		private E e;

		public E getE() {
			return e;
		}

		private Element(E e, int rank) {
			this.e = e;
			this.rank = rank;
		}

		@Override
		public int compareTo(Element<E> o) {
			return this.rank - o.rank;
		}

	}

	private Combinationable<Element<T>> combination = null;
	public CombinationSortByInput(Collection<T> elements) {
		Collection<Element<T>> elementsInput = convertCollection(elements);
		combination = new ComparableCombination<Element<T>>(elementsInput);
		
	}
	@Override
	public List<List<T>> findCombinations(int start, int end) {
		List<List<Element<T>>> elementsOutput = combination.findCombinations(start, end);
		List<List<T>> output = convertListOfList(elementsOutput);
		return output;
	}

	@Override
	public List<List<T>> findCombinations() {
		return findCombinations(0, combination.getElements().size());
	}

	@Override
	public List<List<T>> findCombinations(int size) {
		return findCombinations(size,size);
	}

	private static <T> Collection<Element<T>> convertCollection(Collection<T> input) {
		Collection<Element<T>> elementCollectionInput = new ArrayList<Element<T>>();
		Iterator<T> iterator = input.iterator();
		int i = 0;
		while(iterator.hasNext()) {
			T t = iterator.next();
			Element<T> element = new Element<T>(t, i++);
			elementCollectionInput.add(element);
		}
		return elementCollectionInput;
	}
	
	private static <T> List<List<T>> convertListOfList(
			List<List<Element<T>>> elementsOutput) {
		List<List<T>> output = new ArrayList<List<T>>();
		for(List<Element<T>> elementList : elementsOutput) {
			List<T> tlist = convertList(elementList);
			output.add(tlist);
		}
		return output;
	}



	private static <T> List<T> convertList(Collection<Element<T>> elementList) {
		List<T> tlist = new ArrayList<T>();
		for(Element<T> element: elementList) {
			T t = element.getE();
			tlist.add(t);
		}
		return tlist;
	}
	@Override
	public Collection<T> getElements() {
		return convertList(combination.getElements());
	}
}

顺便附上TestNG unitestcode

package math.combination;

import java.util.Arrays;
import java.util.List;

import math.combination.Combinationable;
import math.combination.ComparableCombination;

import org.testng.annotations.Test;
import org.testng.annotations.BeforeClass;
import static org.testng.AssertJUnit.assertNotNull;
import static org.testng.AssertJUnit.assertEquals;
import static org.testng.AssertJUnit.assertTrue;
public class TestComparableCombination {
	private Combinationable<Integer> combination= null;
	@Test
	public void testGetElements() {
		assertNotNull(combination.getElements());
		assertEquals(3, combination.getElements().size());
	}
	
	@Test
	public void testFindCombinationsSizeZero() {
		List<List<Integer>> lists = combination.findCombinations(0);
		assertNotNull(lists);
		assertEquals(1, lists.size());
		assertNotNull(lists.get(0));
		assertEquals(0, lists.get(0).size());
	}
	
	@Test (expectedExceptions = IllegalArgumentException.class)
	public void testFindCombinationsSizeMinus() {
		combination.findCombinations(-1);
		
	}
	
	@Test (expectedExceptions = IllegalArgumentException.class)
	public void testFindCombinationsStartMinus() {
		combination.findCombinations(-1,2);
		
	}
	
	@Test (expectedExceptions = IllegalArgumentException.class)
	public void testFindCombinationsSizeOverflow() {
		combination.findCombinations(combination.getElements().size() + 1);
		
	}
	
	@Test (expectedExceptions = IllegalArgumentException.class)
	public void testFindCombinationsEndOverflow() {
		combination.findCombinations(0,combination.getElements().size() + 1);
		
	}
	
	@Test (expectedExceptions = IllegalArgumentException.class)
	public void testFindCombinationsStartEndWrongOrder() {
		combination.findCombinations(1,0);
		
	}
	
	@Test
	public void testFindCombinationsSizeTwo() {
		List<List<Integer>> lists = combination.findCombinations(2);
		assertNotNull(lists);
		assertEquals(3, lists.size());
		for(List<Integer> list: lists) {
			assertEquals(2, list.size());
			int element0 = list.get(0);
			int elements1 = list.get(1);
			assertTrue(element0 < elements1);
		}
	}
	
	@Test
	public void testFindAllCombinations1() {
		List<List<Integer>> lists = combination.findCombinations();
		assertNotNull(lists);
		assertEquals(8, lists.size());
		
		for(List<Integer> list : lists) {
			System.out.println(list);
		}
	}
	
	@Test
	public void testFindAllCombinations2() {
		List<List<Integer>> lists = combination.findCombinations(0, combination.getElements().size());
		assertNotNull(lists);
		assertEquals(8, lists.size());
	}
	
	@Test(timeOut=20000)
	public void testPerformance() {
		combination = new ComparableCombination<Integer>(Arrays.asList(3,2,1,4,5));
		for(int i = 0;i < 100000; i++) {
			combination.findCombinations();
		}
	}

	@BeforeClass
	public void beforeClass() {
		combination = new ComparableCombination<Integer>(Arrays.asList(3,2,1));
	}

}

package math.combination;

import java.util.Arrays;
import java.util.List;

import math.combination.CombinationSortByInput;
import math.combination.Combinationable;

import org.testng.annotations.Test;
import org.testng.annotations.BeforeClass;
import static org.testng.AssertJUnit.assertNotNull;
import static org.testng.AssertJUnit.assertEquals;
import static org.testng.AssertJUnit.assertTrue;
public class TestCombinationSortByInput {
	private Combinationable<Integer> combination= null;
	@Test
	public void testGetElements() {
		assertNotNull(combination.getElements());
		assertEquals(3, combination.getElements().size());
	}
	
	@Test
	public void testFindCombinationsSizeZero() {
		List<List<Integer>> lists = combination.findCombinations(0);
		assertNotNull(lists);
		assertEquals(1, lists.size());
		assertNotNull(lists.get(0));
		assertEquals(0, lists.get(0).size());
	}
	
	@Test (expectedExceptions = IllegalArgumentException.class)
	public void testFindCombinationsSizeMinus() {
		combination.findCombinations(-1);
		
	}
	
	@Test (expectedExceptions = IllegalArgumentException.class)
	public void testFindCombinationsSizeOverflow() {
		combination.findCombinations(combination.getElements().size() + 1);
		
	}
	
	@Test
	public void testFindCombinationsSizeTwo() {
		List<List<Integer>> lists = combination.findCombinations(2);
		assertNotNull(lists);
		assertEquals(3, lists.size());
		for(List<Integer> list: lists) {
			assertEquals(2, list.size());
			int element0 = list.get(0);
			int elements1 = list.get(1);
			assertTrue(element0 > elements1);
		}
	}
	
	@Test
	public void testFindAllCombinations1() {
		List<List<Integer>> lists = combination.findCombinations();
		assertNotNull(lists);
		assertEquals(8, lists.size());
		
		for(List<Integer> list : lists) {
			System.out.println(list);
		}
	}
	
	@Test
	public void testFindAllCombinations2() {
		List<List<Integer>> lists = combination.findCombinations(0, combination.getElements().size());
		assertNotNull(lists);
		assertEquals(8, lists.size());
	}

	@BeforeClass
	public void beforeClass() {
		combination = new CombinationSortByInput<Integer>(Arrays.asList(3,2,1));
	}
	
	@Test(timeOut=20000)
	public void testPerformance() {
		combination = new CombinationSortByInput<Integer>(Arrays.asList(3,2,1,4,5));
		for(int i = 0;i < 100000; i++) {
			combination.findCombinations();
		}
	}

}